The best plate armor could stop a longbow arrow. However, it couldn’t stop the storms of arrows that trained longbowmen were capable of unleashing. Even then, arrows usually penetrated weak points in the armor. Come to that, the very best metal breastplates could sometimes kept the earliest handgun bullets from penetrating. It didn’t take much firearms development for that to stop, though.
Armored men, especially well-fed knights who had trained all their lives, were capable of a surprising range of movement in heavy armor. They tired more quickly, but the idea of an armored man being unable to mount his horse, or being unable to rise when he fell, are false. Armored men were crushed to death, but this was usually under the weight of corpses and stricken destriers.
Phalanx fighting is an entirely different school, and while Alexander’s phalanx was based on very light armor, earlier Hoplons wore extremely heavy armor and managed to charge the enemy at a dead run. Also, most of Alexander’s serious fighting was done from horseback, with he and the Companion Cavalry charging headlong into the strongest enemy formation. His battles were usually decided before the infantry phalanxes had finished with each other.
Discarding armor might gain you a little quickness, but it probably won’t give you any real advantage, plus it will make any hit your opponent scores that much more dangerous. Armor provides a lot of protection against small wounds, slips, cuts, glancing blows, and other things that can be stopped even by a padded jacket, but would tear naked skin. It was worn onto the field because, for the most part, it worked, whereas naked people of any sort were uncommon on battlefields because they did not have much military usefulness.